Which graph best depicts a slope of $\dfrac{1}{3}$ ? ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\text{Blue}}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\text{Orange}}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\text{Green}}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\text{Pink}}$
Solution: Remember that the slope corresponds to which direction the line slants, and how much it slants. Because $\dfrac{1}{3}$ is positive, the line should slant upwards as we follow it to the right. The answer is either the $\text{blue}$ or $\text{green}$ graph. In which graph does the y value change by $\dfrac{1}{3}$ if the x value changes by $1$ The ${\text{green}}$ graph best depicts a slope of $\dfrac{1}{3}$.